US 20030074336 A1 Abstract A method is provided for deriving a near-optimal fuzzy automaton for a given separation problem. The method includes the steps of: forming a first generation population (
24) of fuzzy automata, where the first generation population of fuzzy automata includes a plurality of fuzzy automata; performing a mutation operation (28) on each fuzzy automaton in the first generation population of fuzzy automata; reproducing the first generation population of fuzzy automata using a survival of the fittest operation (30, 32, 34); and applying a cross-over operator (36) to the reproduced first generation population of fuzzy automata, thereby yielding a next-generation population of fuzzy automata. A near-optimal fuzzy automaton is identified by evaluating the performance (38) of each fuzzy automaton in the next-generation population; otherwise the methodology is repeated until a near-optimal fuzzy automaton is derived for the given separation problem. Claims(23) 1. A method for deriving a near-optimal fuzzy automaton for a given separation problem, comprising the steps of:
(a) forming a first generation population of fuzzy automata, where the first generation population of fuzzy automata having a plurality of fuzzy automata; (b) performing a mutation operation on each fuzzy automata in the first generation population of fuzzy automata; (c) reproducing the first generation population of fuzzy automata using a survival of the fittest operation; and (d) applying a cross-over operator to the reproduced first generation population of fuzzy automata, thereby yielding a next-generation population of fuzzy automata. 2. The method of 3. The method of 4. The method of 5. The method of 6. The method of evaluating the fitness of each fuzzy automaton in the first generation population of fuzzy automata;
ranking the fuzzy automata in the first generation population of fuzzy automata according to the fitness of each fuzzy automaton; and
reproducing at least one of the fuzzy automata in accordance with a reproduction rule.
7. The method of identifying a set of input signals;
evaluating each of the fuzzy automata in the first generation population of fuzzy automata based on the set of input signals, thereby yielding a confusion matrix for each fuzzy automaton; and
determining a diagonal dominance indicator for each confusion matrix.
8. The method of D=(C _{smallest on-diagonal} −C _{largest off-diagonal})/((C _{smallest on-diagonal} +C _{largest off-diagonal})/2) 9. The method of 10. The method of 11. The method of randomly identifying at least two of the fuzzy automata in the first generation population of fuzzy automata, where each of the two fuzzy automata is defined by one or more matrices each having a plurality of data values;
representing in chromosome form each of the data values in at least one of the matrices in each of the two fuzzy automata; and
applying a crossover operator to at least one matrix in each of the two fuzzy automata, where the crossover operator determines the alleles of crossover between the two fuzzy automata, thereby yielding two next-generation fuzzy automata.
12. The method of 13. The method of 14. The method of ^{S}, U^{R}, U^{E0}, A*, B*), where U^{S }is a matrix of fuzzy state transitions, U^{R }is a matrix of fuzzy output transitions, U^{E0 }is a vector of fuzzy state memberships, A* is a space of input vectors, and B* is a space of output vectors. 15. The method of ^{S}, U^{R}, U^{E0 }of at least two fuzzy automata. 16. The method of evaluating the performance of each fuzzy automaton in the next generation of fuzzy automata in relation to the given separation problem; and
repeating steps (b) thru (d) until at least one fuzzy automaton from the next-generation of fuzzy automata achieves a satisfactory performance level in relation to the given separation problem.
17. The method of 18. A method for generating a next generation of fuzzy automata, comprising the steps of:
providing a first and a second input fuzzy automaton, where each fuzzy automaton is defined by one or more matrices each having a plurality of data values; representing in chromosome form at least one of the matrices in each of the first and second input fuzzy automata; and applying a crossover operator to at least one matrix in each of the first and second input fuzzy automata, where the crossover operator determines the alleles of crossover between the first and second input fuzzy automata, thereby yielding two next-generation fuzzy automata. 19. The method of 20. The method of 21. The method of ^{S}, U^{R}, U^{E0}, A*, B*), where U^{S }is a matrix of fuzzy state transitions, U^{R }is a matrix of fuzzy output transitions, U^{E0 }is a vector of fuzzy state memberships, A* is a space of input vectors, and B* is a space of output vectors, such that the crossover operator is applicable to U^{S}, U^{R}, U^{E0 }of the first and second input fuzzy automata. 22. A method for evaluating the performance of a fuzzy automata, comprising the steps of:
identifying a set of input signals; evaluating the set of input signals using the fuzzy automata, thereby yielding a confusion matrix for each fuzzy automata; and determining a diagonal dominance indicator for each confusion matrix. 23. The method of D=(C _{smallest on-diagonal} −C _{largest off-diagonal})/((C _{smallest on-diagonal} +C _{largest off-diagona}l)/2)Description [0001] The U.S. Government has certain rights in this invention pursuant to the clause at FAR 52.227-12. [0002] 1. Field of the Invention [0003] This invention relates generally to signal classifiers, and, more particularly, to a signal classifier which employs fuzzy genetic learning automata. [0004] 2. Discussion of the Related Art [0005] Typical passive sensor systems which collect wideband signals are receiving an enormous flux of information from a continually evolving signal environment. This enormous flux of information threatens to exceed the capacities of the human signal analysts to analyze the data. As a result, there is a pressing need for artificially intelligent systems which quickly analyze the arriving data stream, and, while so doing, effect machine learning in order to adapt to the continual signal-environmental changes. The intelligent systems should filter the signal data by identifying and separating known signals from the arriving flux of signal information. This potentially reduces the workload for the human signal analyst by allowing him/her to focus attention on signal features which are more likely to contain mission-important information. [0006] Adaptive front-end signal classifiers are generally known in the art. Conventional front-end signal classifiers utilize many inner product-based schemes which compare the arriving signal to a set of basis functions that serve as exemplary signals. These inner product-based schemes may be based on Fourier analysis, wavelets, and/or Gabor transforms. In each of these schemes, the computational intensity is high and there is little flexibility to adapt to a changing signal environment. [0007] Therefore, it is desirable to provide an adaptive signal classifier which learns to identify specific embedded spatiotemporal signals in an arriving signal data stream of an evolving signal environment. More specifically, it is desirable to implement a signal classifier using fuzzy automata. Fuzzy automata generally use min-max aggregation to process the incoming data, thereby obviating the need for highly intense inner product-based comparisons to exemplary signals. Since each fuzzy automata is a language-learning system, only one requirement needs to be imposed on the signals that are to be acquired: a signal needs to be characterizable as occurring in one or more states and transitioning as a whole or partially among some or all states over time. Thus, the formal language framework of fuzzy automata is particularly well-matched to signal separation applications. In addition, the operation of each fuzzy automaton is independent of the durations of the incoming signals. [0008] In accordance with the teachings of the present invention, a method is provided for deriving a near-optimal fuzzy automaton for a given separation problem. The method includes the steps of: (a) forming a first generation population of fuzzy automata, where the first generation population of fuzzy automata includes a plurality of fuzzy automata; (b) performing a mutation operation on each fuzzy automaton in the first generation population of fuzzy automata; (c) reproducing the first generation population of fuzzy automata using a survival of the fittest operation; and (d) applying a cross-over operator to the reproduced first generation population of fuzzy automata, thereby yielding a next-generation population of fuzzy automata. A near-optimal fuzzy automaton is identified by evaluating the performance of each fuzzy automaton in the population; otherwise the methodology is repeated until a near-optimal fuzzy automaton is derived for the given separation problem. [0009] Additional objects, features and advantages of the present invention will become apparent from the following description and appended claims taken in conjunction with the accompanying drawings. [0010]FIG. 1 is a diagram depicting an exemplary signal classifier implemented in accordance with the present invention; [0011]FIGS. 2A and 2B are flowcharts illustrating a method for deriving near-optimal fuzzy automata for a given separation problem in accordance with the present invention; [0012]FIG. 3 is a diagram depicting an exemplary crossover operation between two fuzzy automata in accordance with the present invention; and [0013]FIG. 4 is a flowchart illustrating a method for deriving a signal classifier in an evolving signal environment in accordance with the present invention. [0014]FIG. 1 illustrates an exemplary signal classifier [0015] In operation, the signal classifier [0016] A method for deriving a near-optimal fuzzy automaton for a given separation problem is shown in FIGS. 2A and 2B. In accordance with the present invention, the near-optimal fuzzy automata may then serve as the basis for a signal classifier. First, a separation problem must be identified [0017] Initially, an input set of fuzzy automata is chosen stochastically by pulling elements of S, R, and E [0018] A genetic algorithm is iteratively applied to the population of fuzzy automata until a near-optimal fuzzy automaton is derived for the given separation problem. In general, a genetic algorithm is a model of learning which derives its behavior from a metaphor of the processes of evolution as they occur in nature. In nature, the members of a population are derived from and represented by chromosomes. Likewise, the members of a population of fuzzy automata must be represented in a chromosome paradigm in order to apply a genetic algorithm. [0019] In accordance with the present invention, at least the first three elements of the quintuple U, which are [0020] where each data value is [0021] A mutation operation can then be applied [0022] For illustration purposes, consider a 2 fuzzy automaton where the random entries chosen for mutation are marked with a star as follows: [0023] Thus, there are two data entries where mutation by bit flipping occurs: [0024] One skilled in the art will readily recognize that the above description is merely exemplary of a mutation operation. It is envisioned that other rules may be devised for effecting a mutation operation within the scope of the present invention. [0025] Next, the first generation population of fuzzy automata is reproduced in accordance with a survival of the fiftest operation. As will be more fully explained below, reproduction involves the following three steps: (1) evaluating the fitness [0026] First, each of the fuzzy automata are evaluated for fitness via a fitness function. In a preferred embodiment of the present invention, the fitness of each fuzzy automaton is assessed using a diagonal dominance indicator. While the following description is provided with reference to a particular fitness function, it is envisioned that other known fitness functions fall within the broader aspects of the present invention. [0027] In order to determine a diagonal dominance indicator for a fuzzy automaton, a set of input signals must be identified from the signal environment. The set of input signal are evaluated by each fuzzy automaton in the population, thereby yielding a confusion matrix for each fuzzy automaton. A diagonal dominance indicator is computed for each confusion matrix, where a figure of merit for diagonal dominance, D, is provided as follows: [0028] For illustration purposes, the diagonal dominance indicator for an exemplary confusion matrix of
[0029] is computed as D=(1.17−0.36)/((1.17+0.36)/2)=1.06. As will be apparent to one skilled in the art, a diagonal dominance indicator for a confusion matrix may be computed in accordance with other known figures of merit. [0030] Second, each of the fuzzy automata in the population are ranked according to the fitness of the individual automaton, where the diagonal dominance indicator is indicative of the fitness of an automaton. More specifically, the fuzzy automata are ranked from the fuzzy automata having the largest diagonal dominance to the fuzzy automata having the smallest diagonal dominance. [0031] Third, at least one of the fuzzy automata in the population is reproduced in accordance with a reproduction rule. In accordance with a survival of the fittest approach, the reproduction rule is fashioned such that the highest ranking fuzzy automata are reproduced and the poorest ranking automata are eliminated. For example, given a population of eight fuzzy automata, an exemplary reproduction rule may specify that the two highest ranking automata are duplicated, the four middle ranking automata are maintained, and the lowest two ranking automata are eliminated. This exemplary reproduction rule is illustrated as follows:
[0032] This particular reproduction rule has the advantage of maintaining a constant population size of eight. It is envisioned that other types of reproduction rules fall within the scope of the present invention. [0033] Once the population of fuzzy automata is reproduced in accordance with a survival of the fittest operation, a unique crossover operator may be applied _{Ψ}, which maps the tuple of input automata (U, V), to the tuple of output, next-generation automata (W, X). In other words, the crossover operator may be expressed as
_{Ψ}((U, V))=(W, X)
[0034] As will be described below, only the state transitions .S, the response transitions .R, and the initial states .E are involved in the crossover operation. The spaces A* and B* are not involved in the crossover operation. [0035] In the transform _{Ψ}, the label Ψ is an ordered triple Ψ=(Ψ_{S}, Ψ_{R}, Ψ_{E0}), where Ψ_{S}, Ψ_{R}, Ψ_{E0 }are matrices having the same dimensions as .S, .R, and .E^{0}. The entries in the arrays are numbers from the set {1, 2, . . . , n−1}, such that the entries determine the alleles of the crossover. In other words, the entries determine the points along the chromosomes where crossover is to occur. These matrices are expressed as follows:
[0036] The operation of the transform can be further specified in view of this definition for _{Ψ}. In particular, each element of the fuzzy automata W and X are further expressed in terms of the elements of U and V. For instance, the first element of W, _{W}S, is generated as follows:
[0037] for each data value [0038] The second element of W, [0039] for each data value [0040] The next generation fuzzy automaton, X, is generated in a similar manner. However, in this instance, the front portion of the chromosome comes from V and the tail portion of the chromosome comes from U. Each element of X is further expressed below. The first element of X, [0041] for each data value within [0042] for each data value [0043] for each data value of [0044] For illustration purposes, an exemplary crossover operation is illustrated below. Suppose U and V are as follows:
[0045] [0046] where Ψ [0047] Although the present invention is not limited as such, the above-described crossover operation is applied to the first generation population of fuzzy automata by randomly selecting pairs of fuzzy automata from the population and then applying the crossover operator to each pair of fuzzy automata. For a population of eight fuzzy automata, the crossover operator is applied to four randomly selected pairs of fuzzy automata. In this way, a next generation population of fuzzy automata have been derived for the given separation problem. [0048] Lastly, each of the fuzzy automata in the next generation population is evaluated for performance [0049] A signal environment, ε(π), will typically evolve over time. For an individual signal in the environment, the time variable t may be used to designate “fast time”. However, the signal environment will ordinarily evolve over “slow time” τ (which may also be referred to as epoch). Accordingly, the separation problem Ε(τ) will also typically evolve over time. [0050] Referring to FIG. 4, a method is provided for deriving a signal classifier in an evolving signal environment. As previously described, a single fuzzy automaton at a fixed epoch in history τ must learn to acquire a subset of signals within the environment. In addition, the fuzzy automaton must also not confuse these signals with the other signals in environment. If multiple fuzzy automata are needed to resolve the separation problem Ε(τ) then the separation problem (may be partitioned [0051] In accordance with the present invention, a near-optimal fuzzy automaton may be derived [0052] An aggregate confusion matrix can be formed [0053] The foregoing discussion discloses and describes merely exemplary embodiments of the present invention. One skilled in the art will readily recognize from such discussion, and from the accompanying drawings and claims, that various changes, modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims. Patent Citations
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